In her statement, Ms Sturgeon said: "People that are being admitted to hospital with the symptoms of Legionnaires' disease are generally, at the moment, less ill than had been the case earlier in the outbreak.

"So, we are seeing fewer people, by no means nobody, but fewer people admitted to hospital going into intensive care."

Ms Sturgeon said that one of the cases was being treated in the Highlands and another was being treated in hospital in the north of England. She emphasised that both patients were linked to the Edinburgh outbreak.

The minister said efforts were continuing to trace the source of the disease.

Outbreak - Update on cases

Legionella bacteria is commonly found in sources of water, such as rivers and lakes

24 confirmed cases

37 suspected of having illness

One death

12 patients in intensive care

Five confirmed patients discharged from hospital

One patient being treated in Highlands and another in the north of England

The outbreak covers areas in the south west of the city and health officials believe it is connected to an outdoor source, possibly a cooling tower.

However, the minister conceded earlier in a statement to MSPs that the cause might never be known. She said that it was "not always possible to conclusively determine."

Residents are being leafleted with information on the disease and what they should do if they are worried they could be at risk.

GPs have been provided with information on spotting the signs of infection and a dedicated NHS helpline has been set up on
0800 0858 531.

It is believed that more than 100 people have contacted the special line.

Dr Duncan McCormick, consultant in public health medicine at NHS Lothian, said: "So far we have 61 suspected and confirmed cases and one of them has unfortunately died.

"I think we are hoping to see no further deaths. We are doing everything we can in terms of diagnosis, appropriate treatment and intensive care immediately as required.

"But we can't rule out any further deaths at this stage."

The health secretary's statement in parliament and later to the media followed a meeting of the Scottish government resilience committee on Wednesday, to co-ordinate the official response to the outbreak.

Rare in Scotland

Early indications suggest the infection was the result of a contaminated cloud being emitted from a cooling tower in the south west of the city.

She told MSPs at Holyrood: "In Scotland, we would normally expect to see around 30 to 40 legionella cases each year. Typically around half of these cases are contracted abroad, but we also see indigenous cases, and it is not unusual to see single sporadic cases of community-acquired legionella.

Robert Air died in the Legionnaires' disease outbreak

"Across Europe, outbreaks are not uncommon, with dozens of outbreaks per annum and thousands of cases.

"However, outbreaks of the size we are currently seeing here in Edinburgh are rare in Scotland - the last time we had an outbreak of this scale was, I understand, in the 1980s in Glasgow."

She explained that Legionnaires' disease was an "uncommon but serious form of pneumonia, caused by bacteria that are distributed widely in both natural and artificial water supplies".

Ms Sturgeon said: "In most cases, the disease is caused by the inhalation of water containing the bacteria and common sources can be showers, air conditioning, cooling towers, or humidifiers."

The minister confirmed that officials were also liaising with the Met Office to analyse the impact of temperature and wind speed on plumes from the cooling towers.